Navigation satellite system positioning with enhanced satellite-specific correction information

ABSTRACT

The invention relates to methods, notably carried out by global or regional navigation satellite system (NSS) receivers, which involve receiving satellite-specific, nadir-angle dependent correction information associated with each of at least two NSS satellites among a plurality of NSS satellites. The correction information is useful to correct observed NSS signals, so as to mitigate the effects of satellite-specific, nadir-angle dependent biases in the NSS signals, and thus improve the performance of position determination systems. The invention also relates to methods for generating such correction information, to methods for designing a satellite, to NSS receivers, to apparatuses for generating correction information to be sent to the receivers, and to computer programs and storage mediums.

FIELD OF TECHNOLOGY

The invention relates to global or regional navigation satellite systems(NSS) position estimation methods and devices. The fields of applicationof the methods and devices include, but are not limited to, navigation,map-making, land surveying, civil engineering, agriculture, disasterprevention and relief, and scientific research.

BACKGROUND

Navigation satellite systems (NSS) include both global navigationsatellite systems (GNSS) and regional navigation satellite systems(RNSS), such as the Global Positioning System (GPS) (United States),GLONASS (Russia), Galileo (Europe), BeiDou (China), and the IndianRegional Navigational Satellite System (IRNSS) (systems in use or indevelopment). A NSS typically uses a plurality of satellites orbitingthe Earth. The plurality of satellites forms a constellation ofsatellites. A NSS receiver detects a code modulated on anelectromagnetic signal broadcast by a satellite. The code is also calleda ranging code. Code detection includes comparing the bit sequencemodulated on the broadcasted signal with a receiver-side version of thecode to be detected. Based on the detection of the time of arrival ofthe code for each of a series of the satellites, the NSS receiverestimates its position. Positioning includes, but is not limited to,geolocation, i.e. the positioning on the surface of the Earth.

An overview of GPS, GLONASS and Galileo is provided for instance insections 9, 10 and 11 of Hofmann-Wellenhof B., et al., GNSS, GlobalNavigation Satellite Systems, GPS, GLONASS, Galileo, & more,Springer-Verlag Wien, 2008, (hereinafter referred to as “reference[1]”).

Positioning using NSS signal codes provides a limited accuracy, notablydue to the distortion the code is subject to upon transmission throughthe atmosphere. For instance, the GPS includes the transmission of acoarse/acquisition (C/A) code at 1575.45 MHz, the so-called L1frequency. This code is freely available to the public, in comparison tothe Precise (P) code, which is reserved for military applications. Theaccuracy of code-based positioning using the GPS C/A code isapproximately 15 meters, when taking into account both the electronicuncertainty associated with the detection of the C/A code (electronicdetection of the time of arrival of the pseudorandom code) and othererrors including those caused by ionospheric and tropospheric effects,ephemeris errors, satellite clock errors and multipath propagation.

An alternative to positioning based on the detection of a code ispositioning based on carrier phase measurements. In this alternativeapproach or additional approach (ranging codes and carrier phases can beused together for positioning), the carrier phase of the NSS signaltransmitted from the NSS satellite is detected, not (or not only) thecode modulated on the signal transmitted from the satellite.

The approach based on carrier phase measurements has the potential toprovide much greater position precision, i.e. up to centimetre-level oreven millimetre-level precision, compared to the code-based approach.The reason may be intuitively understood as follows. The code, such asthe GPS C/A code on the L1 band, is much longer than one cycle of thecarrier on which the code is modulated. The position resolution maytherefore be viewed as greater for carrier phase detection than for codedetection.

However, in the process of estimating the position based on carrierphase measurements, the carrier phases are ambiguous by an unknownnumber of cycles. The phase of a received signal can be determined, butthe number of cycles cannot be directly determined in an unambiguousmanner. This is the so-called “integer ambiguity problem”, “integerambiguity resolution problem” or “phase ambiguity resolution problem”,which may be solved to yield the so-called fixed solution.

GNSS observation equations for code observations and for carrier phaseobservations are for instance provided in reference [1], section 5. Anintroduction to the GNSS integer ambiguity resolution problem, and itsconventional solutions, is provided in reference [1], section 7.2. Theskilled person will recognize that the same or similar principles applyto RNSS systems.

In order to improve the positioning process at the receivers, such as toimprove the performance of position determination systems, some systemsinvolve sending correction information to the receivers. Such correctioninformation may generally be seen as comprising information useful tocorrect NSS observations made by a receiver. For example, the correctioninformation may represent data relating to the NSS system that may betaken into account and used to improve the estimation of the receiverposition. The correction information may comprise correction datarelating to NSS satellites, such as, but not limited to, accurateorbital data and accurate satellite clock data to improve thepositioning solution.

The correction information may be computed or prepared by a network ofreference receivers with precisely known positions in a global referenceframe (i.e., coordinate system). A typically world-wide network ofreference receivers is used for GNSS systems, whereas a regional networkof reference receivers is typically sufficient for RNSS systems. Thedata from the reference receivers is transmitted for example over theinternet to a processing centre, where the data is collected,synchronized and processed. During the data processing, a variety ofproducts can be generated, including e.g. satellite orbits, satelliteclock errors, GNSS (or RNSS) measurement biases, and atmosphericeffects. The products (or corrections) are then sent to the roverreceivers on the field. The transmission to the rover can take place inmany different forms, of which the most commonly used are the internetand satellite links. For a descriptive example of a global GNSSpositioning correction service see e.g. WO 2011/034616 A2 (applicantreference: TNL A-2585PCT).

There is a constant need for improving the implementation of positioningsystems based notably on GNSS (or RNSS) carrier phase measurements, toobtain a precise estimation of the receiver position.

SUMMARY

The present invention aims at meeting the above-mentioned needs. Theinvention includes methods and apparatuses as defined in the claims.

In one embodiment of the invention, a method is carried out by a NSSreceiver (or, in an alternative, by a NSS receiver and a processingentity connected to the NSS receiver) to estimate parameters derived atleast from NSS signals useful to determine a position. The methodcomprises the following steps. A NSS signal is observed from each of aplurality of NSS satellites. The method also comprises receivingcorrection information, hereinafter referred to as “satellite-specific,nadir-angle dependent correction information” or, for the sake ofclarity,“satellite-specific-nadir-angle-dependent-correction-information”,associated with each of at least two NSS satellites among the pluralityof NSS satellites. Thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite is useful to correct the observed NSSsignals from the NSS satellite. Specifically, thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite comprises correction informationdepending on the nadir angle of a receiver as seen from the NSSsatellite, so as to mitigate the effects of satellite-specific,nadir-angle dependent biases in the NSS signals transmitted from the NSSsatellite. The observed NSS signals from the plurality of NSS satellitesare then processed by making use of, i.e. based on, thesatellite-specific-nadir-angle-dependent-correction-information.

The satellite-specific-nadir-angle-dependent-correction-information isreceived for each of at least two NSS satellites, such as for examplefor all available NSS satellites or for a set of selected NSSsatellites. As will be apparent from the detailed description, ratherthan considering that nadir-angle dependent biases constitute an anomalyaffecting an isolated, unhealthy satellite, to be eventuallydecommissioned due to this anomaly, the inventors have turned a problemupside down by assuming that the signals from a plurality of NSSsatellites, possibly all NSS satellites, are affected by nadir-anglebiases. In doing so, a problem has been turned into an opportunity tosignificantly improve the positioning capabilities of NSS receivers, andto provide relaxed requirements for designing NSS satellites.

While some embodiments of the invention relate, as explained above, tothe use of correction information by NSS receivers, other embodiments ofthe invention relate to generating correction information to be used,later, by NSS receivers.

In one embodiment, a method is provided for generatingsatellite-specific-nadir-angle-dependent-correction-information, saidcorrection information being associated with each of at least two NSSsatellites among a plurality of NSS satellites. The satellite-specific,nadir-angle dependent correction associated with a NSS satellitecomprises correction information depending on the nadir angle of areceiver as seen from the NSS satellite, and such correction informationis useful to mitigate the effects of satellite-specific, nadir-angledependent biases in the NSS signals transmitted from the NSS satellite.The method comprises, for each NSS satellite among the at least two NSSsatellites: (i) receiving raw observations obtained by observing NSSsignals from the NSS satellite from a plurality of reference stations;(ii) computing combination values based on the raw observations tocancel out the effects of the satellite motion relative to the referencestations (i.e., to cancel out the effects of what is known in the art asthe “geometry”), the effects of the clocks (of both the receiver and thesatellite), the effects of the troposphere, and the effects of theionosphere; and (iii) generatingsatellite-specific-nadir-angle-dependent-correction-information based onthe difference between the computed combination values and asatellite-specific reference value that is constant over all nadirangles.

The method provides an effective way to generatesatellite-specific-nadir-angle-dependent-correction-information that maybe sent to, and used by, NSS receivers to mitigate the effects ofsatellite-specific, nadir-angle dependent biases in the NSS signalstransmitted from NSS satellites.

The invention also relates to NSS receivers configured to carry out theabove-mentioned method to estimate parameters derived at least from NSSsignals useful to determine a position. The invention further relates toapparatuses configured for carrying out the above-described method forgeneratingsatellite-specific-nadir-angle-dependent-correction-information. Theinvention also relates to systems comprising apparatuses for generatingthe above-mentioned correction information and receivers using saidinformation.

Yet furthermore, the invention relates to methods for designing a NSSsatellite or a sub-system thereof, as defined in the claims. Namely, theinvention also relates, in one embodiment, to a method for designing,using a satellite design program, any one of a NSS satellite and asubsystem thereof, wherein the method comprises a step of making adesign of the NSS satellite or the subsystem thereof respectively, inwhich, for at least one frequency, the delays of the signals radiatedover different nadir angles of the radiation pattern of the satellite'santenna designed to be, in orbit, directed towards the Earth, are takeninto account by the satellite design program to decide whether a designof a NSS satellite or of a subsystem thereof is acceptable.

The invention also relates, in some embodiments, to computer programs,computer program products, and storage mediums for storing such computerprograms, comprising computer-executable instructions for carrying out,when executed on a computer such as a NSS receiver or on anotherapparatus, the above-mentioned methods.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention shall now be described, inconjunction with the appended drawings in which:

FIG. 1 is a flowchart a method according to one embodiment of theinvention, wherein the method is carried out by a NSS receiver, or, inan alternative, by a NSS receiver and a processing entity connectedthereto;

FIG. 2 schematically illustrates a satellite orbiting the Earth, as wellas a NSS receiver on Earth, to illustrate the concepts of nadir angleand elevation angle;

FIG. 3 schematically illustrates a NSS receiver in one embodiment of theinvention;

FIG. 4 is a flowchart a method for generatingsatellite-specific-nadir-angle-dependent-correction-information, in oneembodiment of the invention;

FIG. 5 is a flowchart of a portion of a method for generatingsatellite-specific-nadir-angle-dependent-correction-information, in oneembodiment of the invention;

FIG. 6 schematically illustrates an apparatus configured for generatingsatellite-specific-nadir-angle-dependent-correction-information, inaccordance with one embodiment of the invention;

FIG. 7 schematically illustrates a portion, namely a so-calledgenerating unit, of an apparatus configured for generatingsatellite-specific-nadir-angle-dependent-correction-information, inaccordance with one embodiment of the invention;

FIG. 8 shows the observed satellite wide-lane biases, in meters, in thesignals transmitted by some BeiDou satellites (among satellites C01 toC35) over a period of one week;

FIG. 9 shows the observed satellite wide-lane biases, in meters, in thesignals transmitted by some GPS satellites (among satellites G01 to G37)over a period of one week;

FIG. 10 shows the ionosphere-free pseudorange (PC) and phase (LC)combinations, i.e. “PC-LC”, for one BeiDou satellite (C13) observed byone receiver (BKK9) over time, together with the satellite elevation asseen from the receiver;

FIG. 11 shows the ionosphere-free pseudorange (PC) and phase (LC)combinations, i.e. “PC-LC”, for one GPS satellite (G21) observed by onereceiver (BKK9) over time, together with the satellite elevation as seenfrom the receiver;

FIG. 12 shows a multipath combination based on observations from onereceiver (Station COCO) as a function of time for a BeiDou satellite(C11);

FIG. 13 shows a multipath combination based on observations from onereceiver (Station COCO) as a function of the elevation angle in degreesfor a BeiDou satellite (C11);

FIG. 14 schematically illustrates how computed combination values may beassigned into angle bins in one embodiment of the invention;

FIG. 15 schematically illustrates exemplary power envelopes of asatellite, in order to understand, or partially understand, the possibleorigin of the detected nadir-angle biases addressed by embodiments ofthe invention;

FIG. 16 schematically illustrates two exemplary rings of antennas, alsoin order to understand, or partially understand, the possible origin ofthe detected nadir-angle biases addressed by embodiments of theinvention; and

FIG. 17 schematically illustrates exemplary radiation patterns of tworings of antennas (inner and outer), as well as a total radiationpattern for a satellite's antenna system, in order to further theunderstanding of the possible origin of the detected nadir-angle biasesaddressed by embodiments of the invention.

DETAILED DESCRIPTION

The present invention shall now be described in conjunction withspecific embodiments. The specific embodiments serve to provide theskilled person with a better understanding, but are not intended to inany way restrict the scope of the invention, which is defined byappended claims. In particular, the embodiments described independentlythroughout the description can be combined to form further embodimentsto the extent that they are not mutually exclusive.

Throughout the following detailed description, and in the drawings, theabbreviation “GNSS” is used. The invention is, however, not limited toglobal navigation satellite systems (GNSS) but also applies to regionalnavigation satellite systems (RNSS). Thus, it is to be understood thateach occurrence of “GNSS” in the following can be replaced by “RNSS” toform additional embodiments of the invention.

The flowchart of FIG. 1 illustrates a method in one embodiment of theinvention. In this embodiment, the method serves to estimate parameterswhich are derived at least from global navigation satellite system(GNSS) signals and which are useful to determine a position, such as theposition of a rover receiver or reference station. The method mayeventually lead to determining or estimating the rover position orreference station position.

The method involves the use of correction information in the positioningprocess and, in particular, comprises the following steps.

In step s10, a GNSS signal is observed from each of a plurality of GNSSsatellites. The receiver may receive at least one GNSS signal from eachof a plurality of GNSS satellites by observing the ranging codes carriedon a particular frequency by each of the plurality of GNSS satellites,or by observing the phase of the carrier emitted on a particularfrequency by each of the plurality of GNSS satellites, or by observingboth the ranging codes and the carrier phases.

In step s20, the receiver receives correction information, which isherewith called“satellite-specific-nadir-angle-dependent-correction-information”. Thesatellite-specific-nadir-angle-dependent-correction-information isassociated with each of at least two GNSS satellites among the pluralityof GNSS satellites. In particular, thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a GNSS satellite is useful to correct the observed GNSSsignals from the GNSS satellite. Thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a GNSS satellite comprises correction information, suchas for example correction coefficients, which depends on the nadir angleof a receiver as seen from the GNSS satellite. The correctioninformation can be used to mitigate the effects of satellite-specific,nadir-angle dependent biases in the GNSS signals received from the GNSSsatellite. Thesatellite-specific-nadir-angle-dependent-correction-information may forexample be broadcast and received through a wired or wireless network(such as the internet) or via a satellite link.

The correction information may be in the form of, but not limited to, acalibration table or a polynomial expression. A calibration table isparticularly advantageous as it does not require any assumption as towhether the nadir-angle dependent biases are following any specificpattern.

In step s30, the receiver processes the observed GNSS signals from theplurality of GNSS satellites by making use of, i.e. based on, thereceivedsatellite-specific-nadir-angle-dependent-correction-information. Inparticular, GNSS signals at different frequencies, from different GNSSsatellites may be combined to ultimately compute the position of thereceiver. Step s30 is known in the art except for the use of thesatellite-specific-nadir-angle-dependent-correction-information in thepositioning process, in order to correct the observations or dataderived therefrom.

Based on the outcome of processing step s30, parameters are estimated,which are useful to determine or estimate a position, such as theposition of a rover (or reference station) or more specifically theposition of the antenna thereof. For instance, the estimated parametersmay indicate the most probable number of cycles along a carrierseparating a GNSS satellite from the GNSS receiver, i.e. the estimatedparameters may be the resolved integer ambiguity. In other words, theoutput of the method need not be the position itself but parameters thatmay be used, for instance by another entity (such as a processing entityon a server dedicated to such task), to estimate or determine the roverposition (or the position of a reference station).

The method may be performed by the receiver itself or by anotherprocessing entity remotely located from, but connect to, the receiver.The receiver may send data representing the GNSS observations to theprocessing entity which is then in charge of receiving thesatellite-specific-nadir-angle-dependent-correction-information (steps20) and processing the observed signals based on, i.e. by making useof, the received correction information (step s30).

The method illustrated by FIG. 1 is advantageous in that it leads to animproved precise positioning. Observations from GNSS satellites thatcould not be used due to nadir-angle biases can now be used in thepositioning process, and observations from GNSS satellites that could beused despite including nadir-angle biases can now be corrected beforebeing used in the positioning process.

Further, in the method of FIG. 1,satellite-specific-nadir-angle-dependent-correction-information isprovided to a receiver for more than one satellite. This means thatnadir-angle dependent biases are not regarded as a phenomenon affectingan isolated, unhealthy satellite (to be eventually decommissioned), butthe nadir-angle dependent biases are regarded as an opportunity toimprove the positioning process for a plurality of satellites. To thatend, correction information is generated and integrated in thepositioning process.

FIG. 2 schematically illustrates a satellite orbiting the Earth and areceiver on or near the Earth's surface. The nadir angle, referred to bythe Greek letter α (alpha), is the angle formed by the (imaginary) linefrom the satellite to the Earth's centre and the (imaginary) line fromthe satellite to the receiver. The elevation angle, referred to by theGreek letter β (beta), is the elevation angle of the satellite withreference to the horizon, as seen from the receiver.

A skilled person will therefore recognize that any reference to thenadir angle within the context of the present invention, and thereforewithin the present document, can be translated into a reference to anelevation angle. The elevation angle is usually taken when thereceiver's perspective is chosen, whereas the nadir angle is moresuitable when the satellite's perspective is taken. To explain thepossible cause of the satellite-specific, elevation- or nadir-anglebiases, the inventors have chosen to take the satellite's perspective,and therefore to talk about the nadir-angle dependence rather than theelevation-angle dependence. Although this approach is counter-intuitivesince the purpose of the method is to estimate the position of thereceiver, the approach helps to better understand the invention.

In one embodiment, the method uses carrier phase and pseudorangemeasurements of the GNSS signals and the candidate sets of integerambiguities are processed to estimate parameters useful to determine theposition.

In one embodiment, the method relates to an absolute positioning processrather than a relative positioning process.

In one embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two GNSS satellites comprisesfrequency-specific correction information. This embodiment isadvantageous in that it has been observed that, for a GNSS satellite,the nadir angle biases may depend on the frequency of the GNSS signalunder consideration.

In one embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationcomprises correction information associated with each of the pluralityof GNSS satellites.

In one embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationcomprises correction information associated with at least one BeiDouGNSS satellite. The correction information may also comprise, in oneembodiment, correction information associated with a majority of theoperational BeiDou GNSS satellites or, in another embodiment, correctioninformation associated with all operational BeiDou GNSS satellites.These embodiments are particularly advantageous in that it has beenobserved that, for at least some BeiDou satellites, the nadir anglebiases are comparatively high, to the point of making it impossible, orat least very difficult, to use observe signals from such satellites ina precise point positioning system with ambiguity resolution. Theinvention is, however, in some embodiments, not limited to BeiDousatellites, and may be applied to any GNSS satellites, including currentand future satellites.

In one embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationcomprises correction information associated with all frequenciesinvolved in the estimation of the receiver position.

In another embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationcomprises correction information associated with one frequency involvedin the estimation of the receiver position.

In yet another embodiment, thesatellite-specific-nadir-angle-dependent-correction-informationcomprises correction information associated with a plurality of, but notall, frequencies involved in the estimation of the receiver position.The correction information may for example be associated with twofrequencies among three available frequencies.

FIG. 3 schematically illustrates an apparatus in one embodiment of theinvention. The apparatus is a receiver 200, which may for example beintegrated in a rover. Receiver 200 comprises a so-called firstreceiving unit 210, a so-called second receiving unit 220, and aso-called processing unit 230. First receiving unit 210 is configuredfor receiving a GNSS signal from each of a plurality of GNSS satellites.Second receiving unit 220 is configured for receivingsatellite-specific-nadir-angle-dependent-correction-information,associated with at least two GNSS satellites. Processing unit 230 isconfigured for processing the observed GNSS signals by making use of,i.e. based on, thesatellite-specific-nadir-angle-dependent-correction-information.Receiver 200 may further comprise means (not illustrated in FIG. 3) fordetermining the receiver's position (or the receiver antenna's position)based on the output of processing unit 230.

While first receiving unit 210 is hosted in receiver 200, secondreceiving unit 220 and processing unit 230 may be hosted on an apparatuslocated remotely from, but connected to, receiver 200. In other words,second receiving unit 220 and processing unit 230 need not be hosted onreceiver 200.

FIG. 4 is a flowchart of a method in one embodiment of the invention,for computingsatellite-specific-nadir-angle-dependent-correction-information, such asfor example correction coefficients. The method is for example carriedout by means of a computer program executed on a computer, or a set ofcomputers. The method is conducted for example in an office computer andneed not be conducted in real-time. The purpose of the method is togenerate satellite-specific-nadir-angle-dependent-correction-informationassociated with each of at least two GNSS satellites among a pluralityof GNSS satellites. After generating the correction information, thecorrection information may be transmitted to a receiver, such as forexample receiver 200 schematically illustrated in FIG. 3. The correctioninformation may be regenerated from time to time, such as following thelaunch of one or more new GNSS satellites, or to accommodate changes ofthe satellite-specific-nadir-angle-dependent-correction-information overthe lifetime of a GNSS satellite. In other words, the correctioninformation may be generated periodically (such as for example everymonth, every two months, every three months, or every six months) and/orin response to particular events. The correction information mayalternatively be generated continuously, based for example on the rawobservations obtained during the last 15 days (or any other period oftime).

The method of FIG. 4 comprises a step s110 of receiving raw observationsobtained by observing, by a plurality of reference stations, GNSSsignals (for example, over a plurality of consecutive days) transmittedfrom the at least two GNSS satellites. In other words, GNSS signals areobserved by a plurality of reference stations, and raw observations areobtained in such a manner. In that respect, a wide data set, such as forexample observations from 60 reference stations over 20 days, ispreferred. Taking a wide data set helps reducing the local effects, suchas for example multipath effects. In one sub-embodiment, rawobservations from more than 15 reference stations over more than 15 daysare obtained. In another sub-embodiment, raw observations from more than30 reference stations over more than 10 days are obtained. In yetanother sub-embodiment, raw observations from more than 45 referencestations over more than 5 days are obtained.

The raw observations are then used to compute, in step s120, combinationvalues to cancel out the effects of the satellite motion relative to thereference stations (i.e. the effects of the geometry), the effects ofthe clocks, the effects of the troposphere and the effects of theionosphere.

The satellite-specific-nadir-angle-dependent-correction-information isthen generated s130 based on the difference between the computedcombination values and a satellite-specific reference value that isconstant over all nadir angles, especially all operational nadir angles(i.e., those for which the signals reach the Earth's surface or, inother words, for which the satellite is visible from a receiver on Earthor near the Earth's surface in the sense that the phase lock is notlost). It will be apparent from the description below how thissatellite-specific reference value that is constant over all nadirangles may be selected. In general, it can be said that thesatellite-specific reference value that is constant over all nadirangles should preferably be selected in such a way that the datamatching the reference value is characterized by a low noise and arelatively large quantity of observed data. In other words, the nadirangle(s) for which the computed combination values match the constantreference value should not be too small, or the satellite may not bevisible from many reference stations, and not too large as theobservations become noisier as the multipath effects increase.

The generatedsatellite-specific-nadir-angle-dependent-correction-information isrelative rather than absolute. Indeed, the correction information isrelative to the bias at the selected reference angle. The method of FIG.4 is not concerned with computing absolutesatellite-specific-nadir-angle-dependent-correction-information, butrelativesatellite-specific-nadir-angle-dependent-correction-information.

In one embodiment, the correction information is not only generated persatellite, but also per frequency and per arc (range) of nadir angles.

In one embodiment, thesatellite-specific-nadir-angle-dependent-correction-information isgenerated, and broadcast to the receivers, every month. In otherembodiments, the correction information is generated and broadcast everyday, every week, or every two months.

In one embodiment (not illustrated in the drawings), step s120 ofcomputing combination values comprises computing multipath combinationvalues based on the raw observations to cancel out the effects of thesatellite motion relative to the reference stations (i.e. the effects ofthe geometry), the effects of the clocks, the effects of thetroposphere, and the effects of the ionosphere.

In one embodiment (not illustrated in the drawings), step s120 ofcomputing combination values comprises computing Melbourne-Wübbenacombination values based on the raw observations to cancel out theeffects of the satellite motion relative to the reference stations(i.e., the effects of the geometry), the effects of the clocks, theeffects of the troposphere, and the effects of the ionosphere.

In one embodiment (not illustrated in the drawings), step s120 ofcomputing combination values comprises computing ionosphere-freepseudorange-carrier phase (PC-LC) combination values based on the rawobservations to cancel out the effects of the satellite motion relativeto the reference station (i.e. the effects of the geometry), the effectsof the clocks, the effects of the troposphere, and the effects of theionosphere.

In one embodiment (not illustrated in the drawings), step s120 ofcomputing combination values comprises computing the geometry-free, alsocalled “ionospheric”, pseudorange-carrier phase combinations based onthe raw observations to cancel out the effects of the satellite motionrelative to the reference stations (i.e. the effects of the geometry),the effects of the clocks, and the effects of the troposphere. Anotherinformation source is used to cancel out the effects of the ionosphere.This other information source used to cancel out the effects of theionosphere may for example be, or comprise, an ionospheric map.

Let us now turn to FIG. 5, which is a flowchart of one embodiment ofstep s130 of generatingsatellite-specific-nadir-angle-dependent-correction-information.

First, the computed combination values are assigned s130 a into aplurality of nadir-angle ranges. Each of these nadir-angle ranges ishereinafter referred to as an “angle bin”. FIG. 14 shows four exemplaryangle bins. The angle bin data collection is performed per frequency andper satellite.

A reference angle bin is then selected s130 b among the angle bins. Asmentioned above, a reference angle bin with low noise (relative to theother angle bins) and a large quantity of data (relative to the otherangle bins) is preferred to improve the quality of the resultingcorrection information. For example, a reference angle bin around 2.5degrees may constitute a suitable trade-off between the requirement toselect low noise data and the requirement to have a relatively largequantity of data. Reference angle bins other than around 2.5 degrees mayhowever be selected based on the available data.

For each angle bin, a mean combination value is then generated s130 c,by taking the average of all the computed combination values that areassociated with nadir angles that fall within said angle bin. The meancombination value generated for the reference angle bin is thesatellite-specific reference value that is constant over all nadirangles, as mentioned above with reference to FIG. 4.

Then, for each angle bin, the mean combination value generated for theangle bin is normalized s130 d by subtracting the mean combination valuegenerated for the reference angle bin from the mean combination valuegenerated for the angle bin under consideration. In such a manner, anormalized mean combination value is generated for each angle bin.

The correction information is then generated s130 e based on thenormalized mean combination values.

In one embodiment (not illustrated in the drawings), thesatellite-specific-nadir-angle-dependent-correction-information isgenerated s130 in the form of at least one calibration table which maybe sent to a plurality of GNSS receivers. Instead of generating acalibration table, the correction information may also be in the form ofcoefficients for a polynomial expression, where the coefficients are tobe sent to a plurality of GNSS receivers.

FIG. 6 schematically illustrates an apparatus 300 configured forgeneratingsatellite-specific-nadir-angle-dependent-correction-information, inaccordance with one embodiment of the invention. The correctioninformation is associated with each of at least two GNSS satellitesamong a plurality of GNSS satellites. Apparatus 300 comprises aso-called receiving unit 310, a so-called processing unit 320, and aso-called generating unit 330.

Receiving unit 310 is configured for, for each GNSS satellite among theat least two GNSS satellites, receiving raw observations obtained byobserving GNSS signals from the GNSS satellite from a plurality ofreference stations.

Processing unit 320 is configured for, for each GNSS satellite among theat least two GNSS satellites, computing combination values based on theraw observations to cancel out the effects of the satellite motionrelative to the reference stations (i.e., the effects of the geometry),the effects of the clocks, the effects of the troposphere and theeffects of the ionosphere.

Generating unit 330 is configured for, for each GNSS satellite among theat least two GNSS satellites, generatingsatellite-specific-nadir-angle-dependent-correction-information based onthe difference between the computed combination values and asatellite-specific reference value that is constant over all nadirangles.

The apparatus of FIG. 6 and the network used to broadcast the correctioninformation are typically operated as a service to rover operators,while the network operator is typically a different entity than therover operator.

FIG. 7 schematically illustrates a generating unit 330 (as describedabove with reference to FIG. 6) in one embodiment of the invention.

Generating unit 330 comprises (i) a so-called assigning sub-unit 330 aconfigured for assigning the computed combination values into aplurality of nadir angle ranges, each nadir angle range beinghereinafter referred to as an “angle bin”; (ii) a so-called selectingsub-unit 330 b configured for selecting a reference angle bin among theangle bins; (iii) a so-called first generating sub-unit 330 c configuredfor generating, for each angle bin, a mean combination value by takingthe average of all the computed combination values that are associatedwith nadir angles that fall within said angle bin, wherein the meancombination value generated for the reference angle bin is thesatellite-specific reference value that is constant over all nadirangles; (iv) a so-called normalizing sub-unit 330 d configured fornormalizing, for each angle bin, the mean combination value generatedfor the angle bin, by subtracting the mean combination value generatedfor the reference angle bin from the mean combination value generatedfor the angle bin, to generate a normalized mean combination value foreach angle bin; and (v) a so-called second generating sub-unit 330 econfigured for generating correction information based on the normalizedmean combination values.

Let us now further explain the context in which some embodiments of theinvention have been developed, for a better understanding thereof.Further embodiments of the invention are also described.

During the inventors' research to adapt an existing GNSS positioningsystem to take into account BeiDou data, it was found out that it wasvery difficult to get any meaningful result at all, from suchsatellites. A closer examination of the input data (i.e., the rawobservations) led to the finding that, for a given BeiDou satellite, thedifference of the ionosphere-free pseudorange (PC) and phase (LC)combinations, i.e., PC-LC, showed a distinct, unexpected angle-dependentpattern instead of the noisy but constant-average output signal that isexpected according to conventional GNSS theory. In other words, thedependency on the viewing angle was not expected according to the priorart GNSS models. These models assume that the satellite biases arecommon for all the GNSS receivers observing a given satellite.

When the value of the biases depend on the GNSS receiver (i.e., if anangle-dependency exists) to an extent comparable with the measurementnoise level, the effects on the pseudoranges will affect the “precisepoint positioning with ambiguity fixing” approach, which uses theMelbourne-Wübenna (MW) combination of observations, and which alsoincludes pseudoranges. Therefore, when the angle dependency affects thepseudoranges, the MW combination is adversely affected, and thecarrier-phase ambiguity-fixing process as a whole is impaired. This isthe case for at least some, and probably all satellites of the BeiDouconstellation: the angle-dependent bias variations significantly exceedthis measurement noise threshold.

In other words, if this bias angle-dependency effect was not properlymitigated, it would be impossible, or at least very difficult, to carryout a “precise point positioning with ambiguity fixing” method with theBeiDou satellites, and therefore those satellites could not beintegrated within such a positioning system (with the currentlyguaranteed quality levels). Some embodiments of the invention addressthese problems.

However, the problem is not limited to satellites from the BeiDouconstellation. Other GNSS satellites (in use or future) may exhibit thisbehaviour. As GNSS positioning systems are improved and the signal noiselevels are reduced, taking into account bias angle-dependencies willplay an ever increasing role (in the light of theangle-dependency-to-signal-noise ratio) in the improvement of theperformance of precise positioning products.

FIGS. 8 to 13 illustrate the problematic phenomenon that someembodiments of the invention address.

In particular, FIG. 8 shows the bias, in meters, in the signalstransmitted by some BeiDou satellites (among satellites C01 to C35) overa period of one week, whereas FIG. 9 shows the bias, in meters, in thesignals transmitted by some GPS satellites (among satellites G01 to G37)over a period of one week. It can be observed that the bias observed forsignals from BeiDou satellites (FIG. 8) fluctuates much more than thebias observed for signals from individual GPS satellites (FIG. 9).

FIG. 10 shows the ionosphere-free pseudorange (PC) and phase (LC)combinations, i.e. PC-LC, for one BeiDou satellite (C13) observed by onereceiver (BKK9) over time, together with the satellite elevation (solidcurve on the figure) as seen from the receiver. In contrast, FIG. 11shows the ionosphere-free pseudorange (PC) and phase (LC) combinations,i.e., PC-LC, for one GPS satellite (G21) observed by one receiver (BKK9)over time, together with the satellite elevation (solid curve on thefigure) as seen from the receiver. It can be observed that the biasobserved for signals from BeiDou satellites (FIG. 10) significantlydepends on elevation, whereas the bias observed for signals from GPSsatellites does not significantly depend on the elevation (FIG. 11).

FIG. 12 shows a so-called multipath combination (as explained below insection “A. The Multipath combination”) computed based on observationsfrom one receiver (Station COCO) over time for a BeiDou satellite (C11).The multipath combination is very useful to observe the phenomenon,since it eliminates the effects of other factors, such as the geometry,the clocks, the ionosphere and the troposphere. FIG. 13 shows amultipath combination based on observations from the same receiver(Station COCO) as a function of the elevation angle in degrees for aBeiDou satellite (C11). The nadir-angle dependency can be clearlyobserved on FIG. 13. In the light of the prior art GNSS model, thenadir-angle dependency is highly unexpected. The dependency does notdepend on the nature of the receiver.

The method to correct the angle-dependent biases makes use, in oneembodiment of the invention, of the multipath combinations. Sections Ato C below first explain such combinations (including, in sections B andC, methods to correct nadir-angle dependent biases, in some embodimentsof the invention), and then section D explains how the multipathcombinations are used to integrate the angle-dependent GNSS signalbiases into the position estimation process. Section E discusses someembodiments that involve checking the quality of the generatedcorrection information. The possible physical origin of the nadir-anglebiases is then discussed in section F, and how satellite designers canbenefit from the invention is discussed in section G.

A. The Multipath Combination

The “Multipath combination” (Hp), as defined in J. Sanz-Subirana, J.Juan-Zornoza, and M. Hernandez-Pajares, GNSS Data Processing. Volume II:Laboratory Exercises. ESTEC, Noordwijk, The Netherlands: ESAPublications Division (ESA TM-23/2), May 2013 (hereinafter referred toas “reference [2]”), has the following expression:

MP _(i) =P _(i) −L _(i)−2{tilde over (α)}_(i)(L ₁ −L ₂)  (equation 1)

where:

-   -   P_(i): Pseudorange observation on frequency ‘i’ (f_(i)).    -   L_(i), L₁: Carrier phase observations on f_(i) and f₁,        respectively.    -   {tilde over (α)}_(i): Frequency-related constant defined as:

$\begin{matrix}{{\overset{\sim}{\alpha}}_{i} = \frac{f_{1}^{2}f_{2}^{2}}{f_{i}^{2}( {f_{1}^{2} - f_{2}^{2}} )}} & ( {{equation}\mspace{14mu} 2} )\end{matrix}$

In the MP_(i) combination, the P_(i)−L_(i) term cancels out thefrequency-neutral effects such as geometry, clocks and troposphere,while the 2{tilde over (α)}_(i)(L₁−L₂) term cancels out the ionosphericeffects. The remainder is a mix of pseudorange and phase multipatheffects, biases, phase ambiguities, residual wind-up effect and noise.Therefore, plotting the MP_(i) should show a horizontal line withsuperimposed noise. The dominant noise source comes from pseudorangenoise and multipath, and thus the noise sigma figure derived from MP_(i)is roughly the sigma of the overall noise affecting the pseudorange,from the point of view of the receiver being used. However, theinventors have observed that some satellites may exhibit angle-dependentbiases that cause the MP_(i) to deviate from the former, ideal,“horizontal line plus noise” behaviour. This has been particularlyobserved in the case of satellites belonging to the BeiDou/COMPASSconstellation, but this effect may also appear for other GNSSsatellites.

B. Multipath Combination-Based Corrections

The procedure to find and correct the angle-dependent biases essentiallyconsists in finding (for a given angle, frequency and satellitecombination) the difference between the observed MP_(i) values and areference MP_(i) horizontal line.

As explained below in section “C. Computing the corrections”, thisprocedure is carried out taking a given angle as reference. Without lossof generality, that angle may be taken as an elevation angle (receiverpoint of view) or as a nadir angle (satellite point of view).

Now, let us introduce the following new terms: Z_(i)(α), being theangle-dependent effect on pseudorange P_(i), for a given angle α; andζ_(i)(α), being the angle-dependent effect on carrier phase L_(i), for agiven angle α. For the sake of conciseness, these terms will be referredto hereinafter as Z_(i) and ζ_(i), and their angle dependency will beimplicit.

Then, the pseudorange and carrier phase observations may be redefinedas:

P′ _(i) =P _(i) +Z _(i)  (equation 3)

L′ _(i) =l _(i)+ζ_(i)  (equation 4)

where P_(i), L_(i) are the ‘nominal’, or ‘biases-free’ pseudorange andcarrier phases, and P′_(i), L′_(i) are the ‘real’ observations (i.e.,those affected by the angle-dependent biases).

Combining equation 1 with equations 3 and 4, the Multipath combinationaffected by angle-dependent biases becomes:

MP′ _(i) =P′ _(i) −L′ _(i)−2{tilde over (α)}_(i)(L′ ₁ −L′ ₂)  (equation5)

MP′ _(i) =P _(i) −L _(i)−2{tilde over (α)}_(i)(L ₁ −L ₂)+[Z_(i)−ζ_(i)−2{tilde over (α)}_(i)(ζ₁−ζ₂)]  (equation 6)

The terms within square brackets are the angle-dependent terms thatcause the MP′_(i) to deviate from MP_(i), and those are essentially thecorrections generated by using the method described below in section “C.Computing the corrections”. Therefore, the “Multipathcombination-derived correction” DMP_(i) is defined as:

DMP _(i) −Z _(i)−ζ_(i)=2{tilde over (α)}_(i)(ζ₁−ζ₂)  (equation 7)

so that:

MP′ _(i) =P _(i) −L _(i)−2{tilde over (α)}_(i)(L ₁ −L ₂)+[Z_(i)−ζ_(i)−2{tilde over (α)}_(i)(ζ₁−ζ₂)]

MP′ _(i) =MP _(i) +DMP _(i)  (equation 8)

When we apply DMP_(i) to P′_(i), the ‘corrected’ pseudorange P*_(i) isobtained:

P* _(i) =P′ _(i) −CMP _(i)  (equation 9)

and, combining equation 3 and equation 7:

P* _(i) =P _(i)+ζ_(i)+2{tilde over (α)}_(i)(ζ₁−ζ₂)  (equation 10)

Equation 10 states that the pseudorange corrected by following themethod described in section “C. Computing the corrections” below isstill affected by the carrier phase-related angle-dependent biases (incase they exist), so it is not completely free from those errors. Theconsequences of this fact are further explored in section D “TheMelbourne-Wübenna combination”.

C. Computing the Corrections

The process to compute the DMP_(i) corrections, as already explained ina slightly more general manner with reference to FIG. 5, exploits thefact that the result of the MP_(i) combination should be a horizontalline plus noise. Angle-dependent deviations from this ideal are computedusing observations from several reference stations on different days,and averaging those differences within angle “bins” to get correctioncurves. The specific steps, in one embodiment of the invention, are asfollows:

(Step 1) A software tool is used to read raw observations fromobservation files (for instance, files using the well-known RINEXindustry standard format) and several combinations are computed such asmultipath, MW, ionosphere free, etc., as well as elevation and nadirangles. Those results are stored in other intermediate-result files.

(Step 2) The former files are further subdivided into smaller files,first per system and then per satellite. These new files are hereinaftercalled “satellite” files.

(Step 3) Every “satellite” file is examined by plotting the multipathcombination vs. time. Usable, continuous arcs are identified (eithermanually or automatically) and their start and end time tags identified.

(Step 4) With the above-mentioned information, another software tool isused to break down “satellite” files into “arc” files, each containingonly multipath combinations vs. nadir (or elevation) angle for a single,continuous arc of a given satellite-receiver pair.

These “arcs” should, theoretically, be straight horizontal linescontaminated with multipath noise, and the level of these lines isarbitrary (indeed given by carrier phase ambiguities). However, thetheoretical straight, horizontal lines are distorted as a function ofnadir (or elevation) angle.

The extent and nature of this distortion is computed with respect to,i.e. relative to, a previously selected reference nadir/elevation angle,and there is no absolute reference point.

The correction is aimed at eliminating the distortion. Therefore, theresiduals that will appear because of selecting a given reference angleshould be constant, and absorbed by both ambiguities and satellitebiases. Thus, they should not affect further signal processing if thedistortion elimination procedure is carried out in a consistent way forall satellites involved.

(Step 5) All the “arc” files of a given satellite from several days andreceivers are then fed to a software application that will:

(Step 5.a) Open a given arc file, and read the contents, then sortingthe multipath combinations into “angle bins” (as illustrated on FIG. 14)in accordance with their corresponding nadir/elevation angle. An anglebin configuration for nadir angle may for example be 0.5 degrees-widebins, ranging from 0 to 15 degrees (for a MEO satellite).

(Step 5.b) The multipath combination corresponding to a given angle binis stored by adding it to an accumulator variable associated with thatangle bin and satellite. Additional bin-related variables keep track ofthe number of values already stored in every angle bin.

(Step 5.c) When the “arc” file ends, the accumulator for each angle binis divided by the corresponding number of multipath combinations stored,yielding a single value per angle bin: The average of all multipathcombinations within that interval (0.5 degrees in this example), forthat specific satellite arc. The former operation reduces the standardmultipath (i.e., the receiver-environment multipath) as well as thenormal signal noise, with the downside of reducing the angularresolution needed to accurately compute the aforementioned distortion. Abin size between 0.5 and 1.0 degrees is an appropriate trade-off valuefor nadir angle corrections.

(Step 5.d) So far, the per-bin averages have values that are arbitrarybecause they contain the ambiguity related to the arc. Therefore, areference angle bin is selected (manually or automatically), and itsaverage bias value is subtracted from the biases in all the bins. Insuch a way, only normalized average values remain that show how thedistortion is behaving as a function of nadir angle, taking a given,common, nadir angle as reference.

(Step 5.e) Since the multipath combination does not follow a normalprobability distribution, the per-bin averaging process does not get ridof some biases that affect the distortion function to be determined.Thus, the normalized average values previously determined are stored,the “arc” file is closed, and steps 5.a) to 5.d) are repeated for other“arc” files from different epochs and receivers, and stored separately.

(Step 6) When all the available “arc” files for a given satellite (andmultiple receivers and days) are processed, the different average valuesfor a given angle bin are further combined by finding their average.This should mitigate the multipath biases associated with a specificsatellite-receiver-epoch combination.

The result of the above-described method is a file that contains lineswith:

-   -   a) Nadir/elevation angle: The middle point of the angle bin is        given, in degrees.    -   b) The average of all “normalized” arc averages (i.e., the        correction), in meters.    -   c) The standard deviation of the mean (meters), i.e. the STD of        all multipath combinations (for all arcs) going into that        specific angle bin, divided by the square root of the total        number of multipath combinations used in that angle bin. This        provides a metric for overall correction accuracy.    -   d) The total number of multipath combinations (the multipath        combination measurements) used in the angle bin.        D. The Melbourne-Wübenna Combination

The Melbourne-Wübenna combination (MW) is often used to compute severalparameters used by a GNSS positioning engine. This combination is afurther combination of the “widelane” and “narrow-lane” combinations,which are defined as follows. The wide-lane combination is defined as:

$\begin{matrix}{L_{W} = \frac{{f_{1}L_{1}} - {f_{2}L_{2}}}{f_{1} - f_{2}}} & ( {{equation}\mspace{14mu} 11} )\end{matrix}$

The narrow-lane combination is defined as:

$\begin{matrix}{P_{N} = \frac{{f_{1}P_{1}} + {f_{2}P_{2}}}{f_{1} + f_{2}}} & ( {{equation}\mspace{14mu} 12} )\end{matrix}$

The Melbourne-Wübenna combination is defined as:

$\begin{matrix}\begin{matrix}{{MW} = {L_{W} - P_{N}}} \\{= {\frac{{f_{1}L_{1}} - {f_{2}L_{2}}}{f_{1} - f_{2}} - \frac{{f_{1}P_{1}} + {f_{2}P_{2}}}{f_{1} + f_{2}}}}\end{matrix} & ( {{equation}\mspace{14mu} 13} )\end{matrix}$

Using equations 3, 4, 11 and 12, as well as the “nominal”, “real” (′)and “corrected” (*) notation introduced before, the followingexpressions are obtained:

$\begin{matrix}{\; {\zeta_{W} = \frac{{f_{1}\zeta_{1}} - {f_{2}\zeta_{2}}}{f_{1} - f_{2}}}} & ( {{equation}\mspace{14mu} 14} ) \\{Z_{N} = \frac{{f_{1}Z_{1}} + {f_{2}Z_{2}}}{f_{1} + f_{2}}} & ( {{equation}\mspace{14mu} 15} ) \\\begin{matrix}{{MW}^{\prime} = {L_{W}^{\prime} - P_{N}^{\prime}}} \\{=  {L_{W} + \zeta_{W} - ( {P_{N} + Z_{N}} )}\Rightarrow{MW}^{\prime} } \\{= {{MW} + ( {\zeta_{W} - Z_{N}} )}}\end{matrix} & ( {{equation}\mspace{14mu} 16} )\end{matrix}$

The corresponding pseudorange- and carrier phase-related biases (Z_(x)and ζ_(x)) of equations 6 and 16 have opposite signs.

Equation 16 implies that using the procedure described in above sectionC only on the MW′ combination, it is possible to find the MW-onlycorrection DMW:

DMW′−MW′−MW=ζ _(W) −Z _(N)  (equation 17)

Now, the DMP_(i) corrections (equation 7) are only applied topseudoranges, obtaining the “corrected” pseudoranges P*_(i) (equations 9and 10). If those “corrected” pseudoranges are introduced in equation12, the result is:

$\begin{matrix}{\mspace{79mu} {\begin{matrix}{P_{N}^{*} = {\frac{{f_{1}P_{1}^{*}} + {f_{2}P_{2}^{*}}}{f_{1} + f_{2}} =}} \\{=  \frac{\begin{matrix}{{f_{1}( {P_{1} + \zeta_{1} + {2\; {{\overset{\sim}{\alpha}}_{1}( {\zeta_{1} - \zeta_{2}} )}}} )} +} \\{f_{2}( {P_{2} + \zeta_{2} + {2\; {{\overset{\sim}{\alpha}}_{2}( {\zeta_{1} - \zeta_{2}} )}}} )}\end{matrix}}{f_{1} + f_{2}}\Rightarrow }\end{matrix}{P_{N}^{*} = { {\frac{{f_{1}P_{1}} + {f_{2}P_{2}}}{f_{1} + f_{2}} + \frac{{f_{1}\zeta_{1}} + {f_{2}\zeta_{2}}}{f_{1} + f_{2}} + \frac{\begin{matrix}{{2\; f_{1}{{\overset{\sim}{\alpha}}_{1}( {\zeta_{1} - \zeta_{2}} )}} +} \\{2\; f_{2}{{\overset{\sim}{\alpha}}_{2}( {\zeta_{1} - \zeta_{2}} )}}\end{matrix}}{f_{1} + f_{2}}}\Rightarrow \mspace{20mu} P_{N}^{*}  = {P_{N} + ( {\zeta_{N} + {2\; {{\overset{\sim}{\alpha}}_{W}( {\zeta_{1} - \zeta_{2}} )}}} )}}}\mspace{20mu} {{where}\text{:}}\mspace{20mu} {{\overset{\sim}{\alpha}}_{W} = \frac{f_{1}f_{2}}{f_{1}^{2} - f_{2}^{2}}}}} & ( {{equation}\mspace{14mu} 18} )\end{matrix}$

After some manipulation, it can be shown that (see equation 14):

ζ_(N)+2{tilde over (α)}_(W)(ζ₁−ζ₂)=ζ_(W)

Therefore:

P* _(N) =P _(N)+ζ_(W)  (equation 19)

Now, if the P*_(N) “corrected” narrow-lane pseudorange (equation 19) iscombined with the L′_(W) “observed” or “uncorrected” wide-lanecarrier-phase (equation 11) in order to get the MW*(“partially-corrected”) Melbourne-Wübbena combination, the result is:

MW′*=L′ _(W) −P* _(N)=(L _(W)+ζ_(W))−(P _(N)+ζ_(W))

MW′*=L _(W) −L _(N)  (equation 20)

An important conclusion may be drawn from equation 20: The processoutlined on Section C generates pseudorange corrections DMP_(i) that arecontaminated with possible carrier-phase angle-dependent bias terms (seeequation 10). However, those extra terms are nevertheless completelycancelled out when forming the MW combination with the uncorrectedcarrier-phase observations.

So, even though the process described above in section C can be directlyused on the MW combination to generate the MW-only correction DMW(equation 17), it is more useful to compute the pseudorange correctionsDMP_(i) because they both mostly correct the pseudoranges and alsocompletely correct the MW combination.

E. Optional Quality Check Method

In one embodiment, the correctness of the generated correctioninformation is checked. This may be useful notably, but not only, (i) tomake sure that a sufficient number of raw observations has been used forgenerating the correction information, (ii) to make sure that multipatheffects on the reference receivers (used to obtained the rawobservations) were not too high, and/or (iii) to make sure that some ofthe reference receivers have not been subject to intentional orunintentional jamming or interference.

For example, in order to check the correctness of the correctionsgenerated as output from FIG. 4 and FIG. 5, the following method may becarried out.

First, the “Group and Phase Ionospheric Calibration” combination (knownin the art as the “GRAPHIC” combination) is computed from the rawobservation data on at least two frequencies.

The GRAPHIC combination for a given frequency “I” is defined as:

$\begin{matrix}{G_{i} = \frac{P_{i} + L_{i}}{2}} & ( {{equation}\mspace{14mu} 21} )\end{matrix}$

This GRAPHIC “G_(i)” combination is not affected by first orderionosphere effects, and its noise level is roughly half of the originalP_(i) pseudorange. On the one hand, it includes carrier phase-relatedterms like the L_(i) ambiguity and the well-known antenna wind-upeffect. Taking into account equations 3 and 4, the GRAPHIC combinationaffected by the angle-dependent biases becomes:

$\begin{matrix}{G_{i}^{\prime} = \frac{P_{i} + Z_{i} + L_{i} + \zeta_{i}}{2}} & ( {{equation}\mspace{14mu} 22} )\end{matrix}$

Now, selecting signals from any two frequencies (denoted as “1” and “2”here), the difference between the “G′_(i)” combinations on thosefrequencies is computed:

$\begin{matrix}{\begin{matrix}{{\Delta \; G_{12}^{\prime}} = {G_{1}^{\prime} - G_{2}^{\prime}}} \\{=  {\frac{P_{1} + Z_{1} + L_{1} + \zeta_{1}}{2} - \frac{P_{2} + Z_{2} + L_{2} + \zeta_{2}}{2}}\Rightarrow }\end{matrix}{{\Delta \; {G_{12}^{\prime}( {G_{1} - G_{2}} )}} + \frac{( {Z_{1} + Z_{2}} ) + ( {\zeta_{1} - \zeta_{2}} )}{2}}} & ( {{equation}\mspace{14mu} 23} )\end{matrix}$

The importance of equation 23 is that the term to the right is half thedifference between the “Multipath combination-derived corrections”DMP_(i) for frequencies 1 and 2, as defined in equation 7. Therefore,equation 23 becomes:

2ΔG′ ₁₂=2(G ₁ −G ₂)+ΔDMP ₁₂  (equation 24)

The difference (G₁-G₂) is free of ionospheric effects and also cancelsall the geometric, tropospheric, and clock effects. Therefore, theremainder is only composed of the difference of carrier phaseambiguities, receiver and satellite biases, wind-up, and antenna phasecenter effects, plus noise. Since the wind-up and the antenna phasecenter effects can be properly modelled and removed, the difference(G₁−G₂) is an arbitrary constant plus noise.

Taking into account the former paragraph, equation 24 may be re-writtenas:

ΔDMP ₁₂−2ΔG′ ₁₂ ≈K  (equation 25)

The parameter “K” remains an arbitrary constant within a given arc(i.e., while no cycle-slips occur on a received signal).

The importance of equation 25 is that it represents a simple buteffective way to check that the correction information output from themethods illustrated by FIGS. 4 and 5 is indeed of good quality: Thedifference in the corrections for a given pair of frequencies, whensubtracting twice the difference of the GRAPHIC combinations for thosefrequencies, must yield a constant value with some superimposed noise(the standard deviation of such noise is effectively the standarddeviation of the pseudorange noise).

Then, a tolerance value may be set (as a function of pseudorange noise)for how the difference stated in equation 25 is allowed to drift fromthe arbitrary constant “K”. If the drift surpasses the said tolerancevalue, then the width of the angle bins, the number of samples beingused, the number of reference stations being used, the length of theobservation period, or a combination thereof, may be adjusted in orderto bring back the correction values within the preset tolerance.

F. Possible Origin of the Nadir-Angle Dependence

Now, to understand the possible origin of the nadir-angle dependence,reference is made to FIGS. 15 to 17. It should be noted however that theinventors are unable to guarantee that the following provides a completeand correct explanation of this physical phenomenon. This, however, byno means affects the capability of putting the invention into practice.In other words, a complete and correct explanation of the physicalphenomenon is not necessary to benefit from the invention and itsembodiments.

When a GNSS satellite orbits the Earth, the distance between the GNSSsatellite and different points of the Earth's surface differs, asillustrated by FIG. 15. In particular, the distance from the satelliteto a receiver seen by the satellite with a nadir angle close to zero(e.g., “receiver 1” in FIG. 15) is smaller than the distance from thesatellite to a receiver seen by the satellite with a larger nadir angle(e.g., “receiver 2” in FIG. 15). This also means that, for a signal fromthe satellite to reach the Earth surface with a relatively constantpower whatever the point on Earth, the satellite has to emit less powertowards receiver 1 than towards receiver 2.

Exemplary power envelopes are illustrated on FIG. 15 to explain this.Rather than having a power envelope with a constant value depending onthe nadir angle (power envelope “a” in FIG. 15), a satellite's radiationpattern should show a power envelope for which more power is sent forlarger nadir angles, to compensate for the larger distances (powerenvelope “b” in FIG. 15).

Thus, a suitable antenna pattern and specific antenna configurations arerequired. Some satellites comprise two rings of antennas (a phasearray), an inner ring and an outer ring, as illustrated in FIG. 16,which comes from David Goldstein, “Request for Feedback on GPS IIR-20(SVN-49) Mitigation Options”, U.S. Coast Guard Navigation Center, 5 Mar.2010, retrieved on Nov. 29, 2013 fromhttp://www.navcen.uscg.gov/pdf/gps/news/Mar2010_svn49/GPSW_SVN_(—)49_inf_Brief_Mar_(—)2010_Final.pdf(hereinafter referred to as “reference [3]”). The inner ring provides aradiation pattern such as one depicted on the first graph (top) of FIG.17 (one lobe), the outer ring provides a radiation pattern such as onedepicted on the second graph of FIG. 17 (three lobes between −20 and 20degrees), and the resulting radiation pattern provided by both rings ofantennas is depicted on the third graph (bottom) (with larger poweraround about −12 and 12 degrees). FIG. 17 is derived from FIG. 3 of GaryFay, Paul Crampton, “Methodology for Modeling the SVN49 Anomaly forStatic Scenarios”, ION ITM 2011 (hereinafter referred to as “reference[4]”).

Moreover, it is believed that the contributions to the radiated signalfrom the inner ring and the outer ring respectively vary depending onthe nadir angle, that the internal satellite configuration of the innerand outer ring antenna electronic circuits may differ in such a mannerthat the delay to which the signals are subject to differ, this leading,globally, the signal delay to vary depending on the nadir angle. Forexample, satellite internal multipath (caused by reflection by filters,etc.) may also lead the delays associated with the inner and outer ringto differ.

Reference [3] exclusively refers to a single, faulty satellite, i.e. theSVN-49 satellite, wherein there is a L5 filter connected to the J2 port.The SVN-49 satellite has been decommissioned since then, after two yearsof its intended twelve-year operation life, since it was consideredfaulty, due a singular and peculiar design defect. This design defectaffecting the SVN-49 satellite was all the more unique in that it wasdue to a rush to retrofit a conventional GPS satellite for reserving,under the International Telecommunication Union (ITU) rules, the L5frequency. In contrast, embodiments of the invention focus on aplurality of GNSS satellites, such for example an entire constellationof satellites having all the same design.

G. Satellite Design

The invention also relates, in one embodiment, to a method fordesigning, using a satellite design program, any one of a GNSS satelliteand a subsystem thereof. Indeed, as explained above, embodiments of theinvention not only enable GNSS receivers to cope with satellites havingan antenna design causing what might be referred to as “anomalous”angle-dependent patterns (in such as a case, one would speak aboutunintentional nadir-angle dependent biases, and faulty or defectivesatellites), but the invention also enables relaxed requirementsregarding the design of satellites (in such as a case, one would ratherspeak about “intentional” nadir-angle dependent biases). This in turnenables GNSS satellite designers to consider a larger range or selectionof antenna designs and space-qualified components when designing GNSSsatellites, and therefore the design of more robust and/or low-costsatellites.

In one embodiment, such a method comprises a step of making a design ofa GNSS satellite or a subsystem thereof, in which, for at least onefrequency, the delays of the signals radiated over different nadirangles of the radiation pattern of the satellite's antenna designed tobe, in orbit, directed towards the Earth, are taken into account by thesatellite design program to decide whether a design of a GNSS satelliteor of a subsystem thereof respectively is acceptable. In other words, inthis embodiment, when designing a satellite, not only the antennapattern of the satellite is taken into account (which is known in theart) but the delays of the signals radiated over different nadir anglesare also taken into account.

By “satellite design program”, it is referred here to any kind ofsoftware tool for assessing or simulating a design of a satellite or ofa subsystem thereof (taking data representing a satellite design and/orthe specification of individual components or sub-systems underconsideration as input parameters) and then determining whether thedesign meets some requirements. The satellite design program may alsobe, or comprise, any kind of software tool for generating,automatically, a plurality of designs and running a simulation, testingor validation procedure to ensure that the satellite, or one of itscomponents, works within the specifications. A simulation software toolmay for example be ‘Simulink’ (an extension of Matlab by the MathworksCo.). Other packages may be used. When designing radio frequency (RF)electronics or the like, design programs are important. The designprograms may for example work at the component level (selectingcomponents like amplifier, mixers and combiners, which are typical for asatellite) or at the satellite level. Components typically havespecifications which may be inputted to a design program to determinewhether certain conditions or goals are met.

In one embodiment, the delays of the signals radiated over differentnadir angles, as mentioned above, are taken into account by thesatellite design program to decide whether the design of the GNSSsatellite or of the subsystem thereof respectively is acceptable in thesense that the difference

delay_(max)−delay_(min)

is taken into account by the satellite design program to decide (i.e.,determine) whether the design of the GNSS satellite or of the subsystemthereof is acceptable, where delay_(max) is the maximum delay occurringat a nadir angle over a range of nadir angles from 0 to α; anddelay_(min) is the minimum delay occurring at a nadir angle over a rangeof nadir angles from 0 to α.

In one embodiment, the above-mentioned method is such that the satellitedesign program decides that a design of the GNSS satellite or of thesubsystem thereof is acceptable if the difference

delay_(max)−delay_(min) <m _(acceptable),

where m_(acceptable) is a value inputted into the satellite designprogram (or simulation program).

This embodiment enables satellite designers to specify, as input to thedesign program, a relaxed specification regarding the maximum valuem_(acceptable) that the difference delay_(max)−delay_(min) may take,while still leading to an acceptable design, knowing that correctioninformation can be later generated (with the method for generatingcorrection information as discussed above, and illustrated withreference to FIG. 4) and sent to, and used by, the GNSS receivers(thanks to the method for using the correction information as discussedabove, and illustrated with reference to FIG. 1). In other words, theunderlying rationale behind the design method according to thisembodiment is that satellite-specific, nadir-dependent correctioninformation can be generated and made available to the receivers, andthus relaxed specifications can be used.

In one embodiment, for the at least one frequency, m_(acceptable) m isgreater than a quarter of the carrier wavelength of the emitted signal.This embodiment provides a specific value for the relaxed delaydifference permitted by the invention, still enabling the GNSS satellite(to be designed, then later manufactured, launched and operated) to beused in high-precision, carrier-based positioning methods with ambiguityfixing. Embodiments of the invention enable to relax the stringentrequirement that, without the invention, would be that m_(acceptable)would have to be smaller than a quarter of the carrier wavelength of theemitted signal.

In the exemplary case of GPS L1 signals, for carrier phase ranging,m_(acceptable) would have to be 5 cm without the invention. Thanks tothe invention, this requirement is relaxed. Namely the maximum valuem_(acceptable) may be larger than 5 cm, and the ambiguity resolutionprocess may still be reliable and enables accurate GNSS positioning.

Still in the exemplary case of GPS L1 signals, but for pseudorange-basedranging, m_(acceptable) would have to be, without the invention, smallerthan the pseudorange noise as measured by the receiver (for example 25or 50 cm, depending on the receivers). Thanks to the invention, thisrequirement is relaxed. Namely the maximum value m_(acceptable) may belarger than the pseudorange noise (for example 25 or 50 cm), and boththe pseudorange-based ranging and the ambiguity resolution process maystill be reliable and enable accurate GNSS positioning.

In a sub-embodiment, for the at least one frequency, m_(acceptable) isgreater than the carrier wavelength of the emitted signal.

In a yet a further sub-embodiment, for the at least one frequency,m_(acceptable) is greater than five times the carrier wavelength of theemitted signal.

Regarding the maximum delay difference m_(acceptable) supported byembodiments of the invention, there is no specific value that exists.For example, in the case of GPS L1 signals, delay differences above 1.5meter have been tested and are supported. Thus, in one embodiment,m_(acceptable) is greater than five times the carrier wavelength of theemitted signal and there is no upper limit for m_(acceptable). Inanother embodiment, m_(acceptable) is COM comprised between five andfifteen times the carrier wavelength of the emitted signal.

In one embodiment, the above-mentioned method is used for designing aGNSS satellite for use in or near an orbit having a minimum satellitealtitude h with respect to the Earth surface, wherein α is a valuecomprised between

${0.95 \cdot {\arcsin ( \frac{R}{R + h} )}}\mspace{14mu} {degrees}$and${{1.05 \cdot {\arcsin ( \frac{R}{R + h} )}}\mspace{14mu} {degrees}},$

where R is the mean Earth radius. This therefore differs whether GEO,MEO or LEO satellites are designed.

H. Additional Remarks

Any of the above-described methods and their embodiments may beimplemented by means of a computer program. The computer program may beloaded on an apparatus, a rover, a receiver or a network station asdescribed above. Therefore, the invention also relates to a computerprogram, which, when carried out on an apparatus, a rover, a receiver ora network station as described above, carries out any one of theabove-described methods and their embodiments.

The invention also relates to a computer-readable medium or acomputer-program product including the above-mentioned computer program.The computer-readable medium or computer-program product may forinstance be a magnetic tape, an optical memory disk, a magnetic disk, amagneto-optical disk, a CD ROM, a DVD, a CD, a flash memory unit or thelike, wherein the computer program is permanently or temporarily stored.The invention also relates to a computer-readable medium (or to acomputer-program product) having computer-executable instructions forcarrying out any one of the methods of the invention.

The invention also relates to a firmware update adapted to be installedon receivers already in the field, i.e. a computer program which isdelivered to the field as a computer program product. This applies toeach of the above-described methods and apparatuses.

GNSS receivers may include an antenna, configured to receive the signalsat the frequencies broadcasted by the satellites, processor units, oneor more accurate clocks (such as crystal oscillators), one or morecentral processing units (CPU), one or more memory units (RAM, ROM,flash memory, or the like), and a display for displaying positioninformation to a user.

Where the terms “first receiving unit”, “generating unit” and the likeare used herein as units (or sub-units) of an apparatus (such as a GNSSreceiver), no restriction is made regarding how distributed theconstituent parts of a unit (or sub-unit) may be. That is, theconstituent parts of a unit (or sub-unit) may be distributed indifferent software or hardware components or devices for bringing aboutthe intended function. Furthermore, the units may be gathered togetherfor performing their functions by means of a combined, single unit (orsub-unit).

The above-mentioned units and sub-units may be implemented usinghardware, software, a combination of hardware and software,pre-programmed ASICs (application-specific integrated circuit), etc. Aunit may include a central processing unit (CPU), a storage unit,input/output (I/O) units, network connection devices, etc.

Although the present invention has been described on the basis ofdetailed examples, the detailed examples only serve to provide theskilled person with a better understanding, and are not intended tolimit the scope of the invention. The scope of the invention is muchrather defined by the appended claims.

1. Method, carried out by a global or regional navigation satellitesystem receiver, hereinafter abbreviated as NSS receiver, or by a NSSreceiver and a processing entity connected to the NSS receiver, toestimate parameters derived at least from NSS signals useful todetermine a position, the method comprising; observing a NSS signal fromeach of a plurality of NSS satellites; receiving correction information,hereinafter referred to as“satellite-specific-nadir-angle-dependent-correction-information”,associated with each of at least two NSS satellites among the pluralityof NSS satellites, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite is useful to correct the observed NSSsignals from the NSS satellite; and thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite comprises correction informationdepending on the nadir angle of a receiver as seen from the NSSsatellite, so as to mitigate the effects of satellite-specific,nadir-angle dependent biases in the NSS signals from the NSS satellite;and processing the observed NSS signals from the plurality of NSSsatellites by using thesatellite-specific-nadir-angle-dependent-correction-information. 2.Method of claim 1, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisesfrequency-specific correction information.
 3. Method of claim 1, whereinthe satellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with each of the plurality of NSS satellites.
 4. Method ofclaim 1, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with at least one BeiDou satellite.
 5. Method of claim 4,wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with a majority of the BeiDou satellites.
 6. Method of claim5, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with the entire constellation of BeiDou satellites.
 7. Methodof claim 1, wherein the method uses carrier phase and pseudorangemeasurements of the NSS signals. 8.-17. (canceled)
 18. Method fordesigning, using a satellite design program, any one of a navigationsatellite system (NSS) satellite and a subsystem thereof, the methodcomprising: a step of making a design of the NSS satellite or thesubsystem thereof respectively, in which, for at least one frequency,the delays of the signals radiated over different nadir angles of theradiation pattern of the satellite's antenna designed to be, in orbit,directed towards the Earth, are taken into account by the satellitedesign program to decide whether a design of a NSS satellite or of asubsystem thereof respectively is acceptable.
 19. Method of claim 18,wherein said delays are taken into account by the satellite designprogram to decide whether the design of the NSS satellite or of thesubsystem thereof respectively is acceptable in the sense that thedifferencedelay_(max)−delay_(min) is taken into account by the satellite designprogram to decide whether the design of the NSS satellite or of thesubsystem thereof respectively is acceptable, where delay_(max) is themaximum delay occurring at a nadir angle over a range of nadir anglesfrom 0 to α; and delay_(min) is the minimum delay occurring at a nadirangle over a range of nadir angles from 0 to α.
 20. Method of claim 19,wherein the satellite design program decides that a design of the NSSsatellite or of the subsystem thereof respectively is acceptable if thedifferencedelay_(max)−delay_(min) <m _(acceptable), where m_(acceptable) is avalue inputted into the satellite design program.
 21. Method of claim20, wherein, for the at least one frequency, m_(acceptable) is greaterthan a quarter of the carrier wavelength of the emitted signal. 22.-23.(canceled)
 24. Method of claim 19, for designing a NSS satellite for usein or near an orbit having a minimum satellite altitude h with respectto the Earth surface, wherein α is a value comprised between${0.95 \cdot {\arcsin ( \frac{R}{R + h} )}}\mspace{14mu} {degrees}$and${{1.05 \cdot {\arcsin ( \frac{R}{R + h} )}}\mspace{14mu} {degrees}},$where R is the mean Earth radius.
 25. Navigation satellite system (NSS)receiver (200) for estimating parameters derived at least from NSSsignals useful to determine a position, the NSS receiver comprising; afirst unit hereinafter referred to as “first receiving unit”, configuredfor observing a NSS signal from each of a plurality of NSS satellites; asecond unit hereinafter referred to as “second receiving unit”,configured for receiving correction information, hereinafter referred toas “satellite-specific-nadir-angle-dependent-correction-information”,associated with each of at least two NSS satellites among the pluralityof NSS satellites, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite is useful to correct the observed NSSsignals from the NSS satellite; and thesatellite-specific-nadir-angle-dependent-correction-informationassociated with a NSS satellite comprises correction informationdepending on the nadir angle of a receiver as seen from the NSSsatellite, so as to mitigate the effects of satellite-specific,nadir-angle dependent biases in the NSS signals from the NSS satellite;and a third unit, hereinafter referred to as “processing unit”,configured for processing the observed NSS signals from the plurality ofNSS satellites by using thesatellite-specific-nadir-angle-dependent-correction-information.
 26. NSSreceiver of claim 25, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisesfrequency-specific correction information.
 27. NSS receiver of claim 25,wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with each of the plurality of NSS satellites.
 28. NSSreceiver of claim 25, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with at least one BeiDou satellite.
 29. NSS receiver of claim28, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with a majority of the BeiDou satellites.
 30. NSS receiver ofclaim 29, wherein thesatellite-specific-nadir-angle-dependent-correction-informationassociated with the at least two NSS satellites comprisessatellite-specific-nadir-angle-dependent-correction-informationassociated with the entire constellation of BeiDou satellites.
 31. NSSreceiver of claim 25, wherein the NSS receiver is configured to usecarrier phase and pseudorange measurements of the NSS signals. 32.-40.(canceled)
 41. Computer program comprising computer-executableinstructions configured, when executed on a computer, to carry out amethod according to claim
 1. 42. (canceled)